Heat the olive oil in a large pot over medium heat. Add the ground beef and cook until browned, breaking it up with a spoon as it cooks.
Add the sliced leeks and carrots to the pot. Stir and cook for 5 minutes until the leeks soften.
Stir in the cubed potatoes, beef broth, rosemary sprigs, salt, and black pepper.
Bring the mixture to a boil, then lower the heat to a simmer. Cover the pot and cook for 25 minutes until the potatoes and carrots are tender.
Remove the rosemary sprigs before serving. Taste and adjust salt if needed.